ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD.

Solution:

Given: ABC and DBC are isosceles triangles

To Prove: ∠ABD = ∠ACD

Let's join point A and point B.

In △DAB and △DAC,

AB = AC (Given)

BD = CD (Given)

AD = AD (Common side)

∴ △ ABD ≅ △ ACD (By SSS congruence rule)

∴ ∠ABD = ∠ACD (By CPCT)

☛ Check: Class 9 Maths NCERT Solutions Chapter 7

Video Solution:

ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD
 

NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.2 Question 5

Summary:

If ABC and DBC are two isosceles triangles on the same base BC, then △ ABD ≅ △ ACD by SSS congruence and ∠ABD = ∠ACD.

☛ Related Questions:

• In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that: i) OB = OC ii) AO bisects ∠A
• In ΔABC,AD is the perpendicular bisector of BC.Show that ΔABC is an isosceles triangle in which AB=AC.
• ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.
• ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that(i) ΔABE ≅ ΔACF(ii) AB = AC, i.e., ABC is an isosceles triangle.